a specular reflector isn't going to gain us that much over a medium white, and can introduce hot spots. if youv'e ever seen a the interior of a sign you'll notice they're white, like a shop light, where a clear coat on metal would produce a specular coat, it's not that much more efficient, and usually doesn't look as nice, except where you're trying to focus a beam.

Okay, wait- what's the plan with these putative Christmas lights? To string them around the edge of the sign behind it to create a lit "frame" around it?

'Cause if that's the question, forget about sourcing LED lights and just get a bucketload of plain old mini-twinkle lights. I have several strings of those I can donate (I'd rather keep the LED ones I have) and I'm sure many others do, too- not that it matters, because if the total distance around the outside is 48', and we recess the strings by, say, one foot to improve the diffusion of the light which reduces the length to 40', two or three strings is all we need.

I know, fire safety, blah blah blah, but realistically, there is ZERO fire danger from normal twinkle lights over LEDs. If you can indefinitely touch a twinkle light to your lips after it's been on for 2 hours, it isn't going to cause a fire. Ever.

If, on the other hand, the idea is that we use LED twinkle lights to cast light down the face of the wall to provide lighting for art hung on the wall for the show, well, you can use my lights, but my expectations for success there are pretty low. Twinkle lights are designed to be highly omnidirectional and lighting like this really needs something designed for a much higher directionality. Might be a fun project to try, though.

minimal fire danger from direct contact, but that's not how those lamps start a fire, they get a nearby material up to it's combustion temp say by getting covered in dust until they're a nice little baked cocoon that will ignite, or they crack from uneven grime on the glass resulting in a flare of teh filament and igniting said grime. there's a reason the things are not rated for permanent installation. then there's the cheap wiring...

the reduced load of the LEDs means that we can string together the ~1000 lamps we want on one line where as most incandescent strings we'd only get 3-500 before we needed to go to a second power source (not for blowing the circuit, for overpowering the cheap cord, where there's also healthy possibility of fire, moreso if you overload it.

that said the risk of that is bitty, however the problems associated with maintaining incandescent lamps on a constant burn in an inaccessible location are a PITA.

trust me, i've done hundreds of very comparable lighting projects, and serviceability is an issue. we want (ideally) LED lamps, on about 1" spacing about 2-3" in from the perimeter. 100 string leds can be had online for ~5-8 bucks a string.

given my druthers in an ideal world we'd be using somethign very different, but more in the $50-100 a foot price point.